The invention relates to mixing liquids of different viscosities.
When drops of a viscous liquid are mixed into a less-viscous surrounding liquid (e.g., mixing an additive into a polymer melt), the drops will elongate. The elongation proceeds slowly at first, because the liquid in the more viscous drops resists deformation more strongly than does the less viscous surrounding liquid. As a result, the mixing process takes longer and consumes more energy. This situation arises often in polymer blending, wherein rubber or plastic materials are combined to synergize the useful properties of several materials. Polymer blending is often accomplished by melt blending a tumbled mixture of initially nearly spherical pellets of the several polymers.
This type of mixing has been a difficult problem to approach analytically. Even considering an idealized device which imparts a simple shear to a mixture, the distribution of fluid components of different viscosities gives rise to gross changes in actual flow patterns, and the stress, strain and velocity fields depend at any instant upon the geometry of component distribution. Such systems are not presently well understood, except in a severely simplified geometrical configuration known as the parallel-plate model, which is commonly described in polymer processing textbooks (e.g., McKelvey, J. M., Polymer Processing, Wiley & Sons, New York (1962); Tadmor & Gogos, Principles of Polymer Processing, Wiley & Sons, New York (1979)).
The problem of a viscous fluid drop suspended in a less viscous medium in shear was described in Taylor, G. I., "The Viscosity of a Fluid Containing Small Drops of Another Fluid", Proc Roy Soc, A-138, 41-48 (1932). Taylor's analysis predicts that in steady state the drop will experience shear and rotation such that the length and orientation of the drop's principal axes oscillate in an offsetting manner, giving the drop a mildly eccentric ellipsoidal envelope of constant shape and orientation. Other description of a fluid drop in a less viscous medium in shear have grown from Taylor's work: e.g., Bartok & Mason, "Particle Motions in Sheared Suspensions. VIII: Singlets and Doublets of Fluid Spheres", J Colloid Sci, 14, 13-26 (1959) and Rumscheidt & Mason, "Particle Motions in Sheared Suspensions. XII: Deformation and Burst of Fluid Drops in Shear and Hyperbolic Flow", J Colloid Sci, 16, 238-261 (1961).